 Limit of detection

A limit of detection describes how small an analyte amount or concentration an analytical procedure can distinguish from its background with a stated degree of certainty. It depends on the procedure, background variation and chosen decision rule. An analytical blank supplies measurements without the intended analyte contribution; its response need not be exactly zero.^[ref]

A simple model exposes the role of the decision rule. Suppose a single response satisfies $Y\sim N({\mu }_B+ac,{\sigma }^2)$, with known blank mean ${\mu }_B$, positive response slope $a$, analyte concentration $c$ and constant known standard deviation $\sigma$. Choose the detection decision threshold $y_c={\mu }_B+1.645\sigma$. Under the assumed normal distribution, a blank exceeds this threshold about5percent of the time. A sample whose mean merely equals $y_c$ exceeds it only half the time.

To obtain95percent probability of exceeding the same detection decision threshold, its mean must instead lie $1.645\sigma$ above it. The model therefore givesFor $\sigma =2$ response units and $a=4$ response units per micromolar, $c_D\approx 1.645\mu \mathrm{M}$. This is an original equal-variance, single-observation calculation, not a universal laboratory multiplier. Estimated blank uncertainty, unequal variance or a different error criterion changes the calculation. A detection claim also does not by itself establish a precise quantitative estimate of the analyte concentration.